Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C32 ⋊ C4×#100 |
933 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 933 conjugacy classes of subgroups — too many to draw. Only its 158 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|a^2=e,b^2=f,c^2=e,f^2=g,b^a=bd,f^a=fg,d^b=dg,i^b=hi^2,h^c=h^2,i^c=i^2108 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#10591503, #72259861, #72259939 |
| maximal normal subgroup of | C4×#10591503, #72259861, #72259939 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 17796);